# Project #121796 - Discreet Probability Distribution

Need help in verifying the answer, I have already done and completing the ones that I have not done.

Read the following scenario and complete each of the four problem sets below:

Suppose the distribution below represents the probability of a person to make a certain grade in Chemistry 101, where x = the letter grade of the student in the class (A=4, B=3, C=2, D=1, F=0).

 X 0 1 2 3 4 P (X) 0.08 0.22 0.34 0.21 0.15[DG1]

1. Is this an example of a valid probability distribution? Explain your answer.

Yes, this is a valid probability distribution.  It contains a random variable X (0,1,2,3,4,) and by assuming, that each observation of the grades is equally likely to be observed then it is represented by the numbers (0.08, 0.22, 0.34, 0.21, and 0.15) respectively in order with the variable. The sums of all of the probabilities do add up to one (1).

All of the values of x are represented

All of the combinations of grades are represented

2. Determine the probability that a student selected at random would make a C or higher in Chemistry 101.

 Probability of C or higher = P (.34) + P9 (.21), +P (0.15) 0.7 70.00%

3. Determine the mean and standard deviation of the grade distribution.

 μ= 2.13 Standard Deviation = X Grade P (X) X (P X) X-μ (X-μ) 2 (X-μ) 2 P (X) 0 0.08 0 -2.13 4.5369 0.362952 1 0.22 0.22 -1.13 1.2769 0.280918 2 0.34 0.68 -0.13 0.0169 0.005746 3 0.21 0.63 0.87 0.7569 0.158949 4 0.15 0.6 1.87 3.4969 0.524535 Σxp= X (PX) = (X-μ)2 P(x)= 1 2.13 1.3331 μ=ΣxP(x)= 2.13 Σ(x-μ)2P(x)= 1.3331 σ=√Σ (x-μ) 2P(x)=1.154599498

4. Make a NEW table that shows only the probability of students passing or failing (i.e. receiving an F) Chemistry 101.

 Observed Pass Fail Success=S Failure =F or q A 1/5 0.20 1 4/5 0.80 1/5 0.20 B 1/5 0.20 1 C 1/5 0.20 1 D 1/5 0.20 1 F 1/5 0.20 0 Totals 1 1.00 4 1

5. “A professor has 30 students in his or her Chemistry 101 course and wants to determine the probability that a certain number of these 30 students will pass his or her course. “Does this represent a binomial experiment? Explain your answer.

6. Based on the Pass/Fail table, what is the probability that 24 of the 30 students enrolled in Chemistry 101 during the spring semester will pass the course?

7. Determine the mean and standard deviation of the data in the Pass/Fail table.

 Subject Mathematics Due By (Pacific Time) 04/15/2016 02:00 am
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